Dataset for facilitating the calculation of aspect ratio of fibrillated cellulose suspensions based on gel point data

This article describes data related to the research paper “Simplification of gel point characterization of cellulose nano and microfiber suspensions” [1]. The characterization of fibrillated celluloses that include cellulose nano and microfibrils (CMNFs) is a challenge for their production on an industrial scale, requiring easy techniques that control their quality and reproducibility. Gel point is a convenient parameter commonly used to estimate the aspect ratio (AR) of CMNFs. However, this estimation requires many sedimentation experiments, which are tedious and time consuming. The dataset includes all information related to the traditional experiments and to the simplified experiments for estimating gel point and AR based on only one sedimentation experiment. The full data set is useful to select the initial concentration to carry out the experimentation. This dataset also includes the information for the validation of the proposed simplified methodology and shows that the errors are lower than 7% for the gel point calculation and of 3% for the AR estimation. A larger databased of nanocellulose suspensions can be built with the reuse of this data to allow the estimation of nanocellulose properties in a future.


a b s t r a c t
This article describes data related to the research paper "Simplification of gel point characterization of cellulose nano and microfiber suspensions" [1] .The characterization of fibrillated celluloses that include cellulose nano and microfibrils (CMNFs) is a challenge for their production on an industrial scale, requiring easy techniques that control their quality and reproducibility.Gel point is a convenient parameter commonly used to estimate the aspect ratio (AR) of CM-NFs.However, this estimation requires many sedimentation experiments, which are tedious and time consuming.The dataset includes all information related to the traditional experiments and to the simplified experiments for estimating gel point and AR based on only one sedimentation experiment.The full data set is useful to select the initial concentration to carry out the experimentation.This dataset also includes the information for the validation of the proposed simplified methodology and shows that the errors are lower than 7% for the gel point calculation and of 3% for the AR estimation.A larger databased of nanocellulose suspensions can be built with the reuse of this data to allow the estimation of nanocellulose properties in a future. ©

Value of the Data
The aspect ratio (AR) of fibrillated cellulose materials, which encompasses cellulose fibers in different scales including cellulose nano and microfibrils (CMNFs), is a complicated data to be calculated from microscopy images [2] .The length of the fibers is difficult to measure in the images due to the entanglement of fibrillated cellulose forming a three-dimensional network and to the high length/diameter ratio of these materials [3] .
An alternative method is the use of the gel point (Ø g ), defined as the lowest concentration at which all fibers are interconnected in a suspension, forming a self-supporting network [4] .This technique has been previously used for the estimation of the AR in different cellulose materials and CMNFs, but it is very tedious [5][6][7][8] .It requires several sedimentation experiments, which are time consuming when several fibrillated celluloses need to be characterized [1] .
• These data are of value to the scientific community because they provide a simpler and faster method to estimate Ø g , and from this value, the AR and the average length of CM-NFs.
• These data provide the information about the experimentation done for the simplification of the gel point methodology and the AR estimation based on a significant reduction of the sedimentation experiments required.• These data include the validation of the simplification by using different fibrillated cellulose samples.• The data of the different fibrillated celluloses can be reused individually to evaluate the differences in sedimentation and also to improve the range of AR in which the simplification is valid.

Data Description
The dataset is provided as an Excel file (DataGelPointUCM-MU.xlsx) including six sheets.Sheet1 "MATLAB Script" is the script developed to calculate the gel point using the CSAPS function of MATLAB which requires the optimization of the "p" parameter as it is explained in methods.In this script, it is described the points in which the values of sedimentation (initial concentration (C o ) and relative sedimentation height) must be included and also the parameters to optimize the "p" parameter which is not a fix value, and its selection depend on the value of Ø g .
Sheet2 "Co and Hs/Ho of 25 samples" include the raw data used to develop the simplification of the gel point methodology.25 different raw materials have been used for this purpose using at least 4 sedimentation experiments at different C o .
Example1 "Calculation of Co" includes an example to calculate the C o of a fibrillated cellulose using the quadratic fit.Then, with the minimum upper experimental error (UEE) is possible to calculate the estimated Ø g at the Co and the error related to the Ø g using different fits in the CSAPS function (Sheet1).
Sheet3 "Smooth spline" includes the Ø g for the 25 fibrillated celluloses and the seven fits.In addition, the error between the Ø g and the estimated Ø g in the C o in CSAPS is calculated, selecting which is the best one and the correlations between Ø g and C o.
Sheet4 "Aspect ratio" includes the AR calculated for the 25 fibrillated celluloses using the estimation in the C o, opt and the best CSAPS fit.
Sheet5 "Validation" includes the data of the sedimentation experiments for the validation of the optimal interval of C o .

Mathematical simplification
According to Martinez et al. (2001), the gel point can be obtained from the slope near the ordinate axis of the curve that relates the initial concentration of a fibrillated cellulose suspension and the relative height between the sediment and the total height (Hs/Ho), as Eq. ( 1) shows [8] .This curve must be graphed when the samples are completed settle and not depend on the time.Currently, two mathematical methods have been used for the calculation of the gel point: first, the quadratic fit without independent term in which the first degree coefficient is the gel point value; and second, the CSAPS fitting tool in MATLAB that use a smoothing spline with requires the introduction of a smoothing parameter (p) that must be optimized to avoid local fluctuations or and y-intercept far to zero [1] .
The assumption to simplify this methodology requires the replacement of the derivative by an increment between two concentrations ( Eq. ( 2) ).Since the gel point is calculated near the relative height close to zero, the increment is selected between a determined concentration Co(i) and a theoretical concentration of zero C o (0) with a relative height (Hs/Ho(0)) of zero.Therefore, the derivative is approximated as the quotient between the Co(i) and the relative sedimentation height (Hs/Ho(i)).

Materials and experimental method
To characterize the Ø g and the AR of a fibrillated cellulose material with a diameter fiber in the micro or nanoscale the materials required are the following: • CMNFs at initial concentration about 1 wt.% • Crystal violet at 0.1 wt.% • Deionized water • 250 mL graduated cylinders • Magnetic stirrer To prepare the CMNF suspension that allow the calculation of the Ø g at a certain C o , an amount of CMNF gel is weighted and diluted in deionized water up to 250-260 mL.200 μL of 0.1 wt.% crystal violet, that do not affect in the sedimentation of the sample, is added to dye the fibrillated suspensions.The suspension is stirred using magnetic agitation until no clusters were observed and avoiding intense agitations that break the fibers.250 mL of the suspension are added into a graduated cylinder and settled until the sediment reach a steady value to obtain the complete deposition of fibrillated cellulose.This methodology is the same in the case of the traditional Ø g using several sedimentation experiments (and the CSAPS or quadratic fit to obtain the gel point) or for the simplified one with required only one experiment in which Ø g is calculated using Eq.(2) .
A total of 25 CMNF samples have been used to study the assumptions to simplify this methodology.Data of most of them have been used in previous publications for other purposes.Their manufacturing methods are briefly summarized below in Table 1 .

Selection of the optimal smoothing spline in the CSAPS fit of MATLAB
To select the optimal smoothing spline, first of all, the "p" parameter" must be optimized for first time.This parameter "p", ranging from 0 to 1, must be adequately chosen.Low "p" parameter values show in the graph Co vs. Hs/Ho a y-intercept far from zero and a linear trend that falsifies the Ø g , whereas a too high "p" parameter value shows a y-intercept close to zero but with local fluctuations (the graph try to connect the experimental values without obtaining a second order curve) [1] .Therefore, the optimal parameter is an intermediate "p" value" which is not a fix value and differs with the Ø g .For this reason, a MATLAB script ( Fig. 1 , Sheet1 of Excel Data Base) was developed to study the best p-value to obtain a low error (respect to the origin) in the y-intercept of the graph Co vs. Hs/Ho, but at the same time there are no local fluctuations.25 fibrillated celluloses (traditional sedimentation values shown in Sheet 2 of Excel Data Base) were studied using the traditional sedimentation curves to evaluate the best fit in CSAPS of MATLAB.
To evaluate the best "p" parameter condition, the Ø g obtained with each "p" condition where compared with the optimal initial concentration (C o,opt ).As Fig. 2 shows, the C o,opt is selected in the point in which the upper experimental error (UEE) is minimum (UEE is represented with the dashed green line of Fig. 2 ).Example 1 of Excel data base shows an example to calculate C o,opt.To obtain this UEE due to the visualization of the settle, we assume an estimated error of Hs ±1 mL.Ø g in the UEE is recalculated using Eq. ( 2) but replacing Hs by Hs ±1.The C o,opt. is selected in the point in which the Ø g in the UEE is the minimum value.
In the Example 1 of Excel data, for this C o,opt. the estimated Ø g was compared with the gel point traditionally calculated with several sedimentation experiments for two different conditions of "p parameter".The first condition to obtain the "p" parameter was a Ø g with a yintercept < |0.0015 •Øg|and another with a y-intercept < |0.005 •Øg|.In the first case, we obtain a Ø g error of 3.3%, whereas in the second case the error increase up to 7.7%.

Table 2
Linear fit between Co, opt and Øg for each percentage used to choose the "p" parameter.

Table 3
Recommendations in the selection of the initial concentration (Co ).
Pretreatments Recommendations Refining 0.05-0.5 kg/m 3 , using lower Co values as refining and main mechanical treatment intensities increases.Enzymatic 0.2-0.5 kg/m 3 AR is very similar after this pretreatment and after the main mechanical treatments of fibrillation.

Powder
Co > 1 kg/m 3 .The decrease in length produces lower AR and higher Øg.TEMPO-mediated oxidation 0.5-3 kg/m 3 , using higher Co values as the oxidant dose increases and as mechanical treatment intensity increases Sheet 3 of Excel data base shows for the 25 fibrillated celluloses the estimated Ø g in the C o,opt and the Ø g using seven conditions of "p" parameter.Table 2 indicates the linear fit between C o,opt and Ø g for each percentage used to choose the "p" parameter.The best correlation to obtain the "p" parameter is when the y-interception is selected under 0.15% of the Ø g due to the lower relative error and the best correlation.
The most important point in this simplification is the selection of the C o , that is a key factor to obtain an adequate estimation of Ø g .The selection of the C o, opt depends on several factors as the raw material, the pretreatments or the intensity of the mechanical treatments.Therefore, in the gel point simplification the initial C o is an arbitrary value that has to be selected based mainly on the experience with other similar fibrillated cellulose or according to some recommendations based on the pretreatment and main mechanical treatments employed to obtain the fibrillated cellulose as Table 3 shows.Therefore, once selecting the C o and calculated the estimated Ø g , it is possible to calculate, with the optimal equation of Table 2 , the C o, opt and compared it with the C o .
In the case the values of C o and C o, opt are too different, where C o is outside of the interval (0.5 •C o, opt, 1.5 •C o, opt ), a second sedimentation experiment is required using a new C o closer to C o, opt, repeating the above steps again.According to the method validation, in the cited interval of C o, opt the Ø g error is under 7% in the fibrillated celluloses used to validate this method.
From the gel point value and assuming a density of the cellulose of 1500 kg/m 3 , it is possible to calculate the average AR of the CMNFs according to the Crowding Number (CN) and to the Effective Medium Theory (EMT) using Eq.(3) and Eq. ( 4) , respectively [2 , 11 , 12] .This information is included in Sheet4 of Excel data base.For this determination, the error in the same interval of Co, opt is under 3% for the samples used to validate the methodology.Finally, with the value of AR (length/diameter ratio) and the determination of the diameter range of the fibrillated cellulose using microscopy images, it is possible to calculate an average length of the fibrillated cellulose, as long as the samples are homogeneous, and avoiding the difficulties of the entanglement of the fibers in the measure of their length.4 shows the Ø g of the fibrillated celluloses using the smoothing spline with an y-interception < 0.0015 •Ø g and the AR using the CN and EMT theory.Then, with the C o,opt of each sample (calculated as Example 1) the estimated Ø g and AR are calculated and compared with the original.It is possible to observe that CN and EMT theories, previously developed by other authors, show differences around 10% in AR when the AR is up to 80, whereas these differences are bigger in shorter AR fibers.However, the AR compared among the Ø g and estimated Ø g are scarce and similar, not being the theory chosen to calculate the AR a relevant parameter.
Finally, Table 5 shows the Ø g and the AR using Eq. ( 2) with initial concentrations that are in the defined interval in which it is not necessary a second sedimentation experiment (0.5 •C o, opt , 1.5 •C o, opt ).It is possible to observe that the error is under 7% for all Ø g calculated and under 3% for the AR.Independently the theory used to calculate the AR, these errors are in the same order.On the other hand, when C o is out of the mentioned interval, in some cases we obtain errors above the 7 and 3%, respectively.

Fig. 1 .
Fig. 1.Script to obtain Øg according to a determined (y-interception < percentage •100 •Øg).In the script shown the selection of the y-interception was under 0.15% of Øg (y-interception < 0.0015 •Øg), that would be the optimal value.

Fig. 2 .
Fig. 2. Estimation of gel point values (Øg ) vs. Initial concentration selected (Co ).Comparison of traditional and simplified methods and experimental error limitations.

Table 1
List of raw materials and treatments to produce the CMNFs used in this study.

Table 4
Gel point (Øg ) and AR.As indicated in the limitations, this value in the equations of Table2is out of range due to the AR is under 20-30. *